摘要 :
It is well known that the standard finite element method (FEM) with overly-stiff effect gives the upper bound solutions of natural frequencies in the free vibration analysis using triangular and tetrahedral elements. In this study...
展开
It is well known that the standard finite element method (FEM) with overly-stiff effect gives the upper bound solutions of natural frequencies in the free vibration analysis using triangular and tetrahedral elements. In this study, for the first time, this paper aims to improve the prediction of eigenfrequencies through the perfect match between the stiffness and mass matrices. With redistribution of mass in the system, we can tune the balance between stiffness and mass of a discrete model. This can be done by simply shifting the integration points away from the Gaussian locations, while ensuring the mass conservation. A number of numerical examples including 2D and 3D problems have demonstrated that the accuracy of eigenfrequencies is strongly determined by the location of integration points in the mass matrix. With appropriate selection of integration points in the mass matrix, even the exact solution of eigenfrequencies can be obtained in both FEM and smoothed finite element method (SFEM) models.
收起
摘要 :
Green element method (GEM) is a numerical approach that combines boundary element method (BEM) and finite element method (FEM), which is effective to solve many physical problems, such as diffusion equation, heat transfer equation...
展开
Green element method (GEM) is a numerical approach that combines boundary element method (BEM) and finite element method (FEM), which is effective to solve many physical problems, such as diffusion equation, heat transfer equation, etc. This paper proposes a novel GEM named mimetic GEM, which utilizes discrete flux operator derived from mimetic FDM to approximate boundary integral of the product of fundamental solution and edge-normal flux in GEM. Proposed mimetic GEM is indeed a novel numerical method mixing the ideas of BEM, FEM, and mimetic FDM, which The method synthesizes some typical advantages of traditional numerical methods, that has a semi-analytical accuracy same as BEM. The method can be adaptive to unstructured grid same as FEM, and has a good convergence same as FDM.
收起
摘要 :
Mixed finite element methods with flux errors in H(div)-norms and div-least-squares finite element methods require a separate marking strategy in obligatory adaptive mesh-refining. The refinement indicator sigma(2)(T, K)=eta(2)(T,...
展开
Mixed finite element methods with flux errors in H(div)-norms and div-least-squares finite element methods require a separate marking strategy in obligatory adaptive mesh-refining. The refinement indicator sigma(2)(T, K)=eta(2)(T, K)+mu(2)(K) of a finite element domain K in an admissible triangulation T consists of some residual-based error estimator eta(T, K) with some reduction property under local mesh-refining and some data approximation error mu(K). Separate marking means either Dorfler marking if mu(2)(T) <= kappa eta(2)(T) or otherwise an optimal data approximation algorithm with controlled accuracy. The axioms are sufficient conditions on the estimators eta(T, K) and data approximation errors mu(K) for optimal asymptotic convergence rates. The enfolded set of axioms of this paper simplifies [C. Carstensen, M. Feischl, M. Page, and D. Praetorius, Comput. Math. Appl., 67 (2014), pp. 1195-1253] for collective marking, treats separate marking established for the first time in an abstract framework, generalizes [C. Carstensen and E.-J. Park, SIAM J. Numer. Anal., 53 (2015), pp. 43-62] for least-squares schemes, and extends [C. Carstensen and H. Rabus, Math. Comp., 80 (2011), pp. 649-667] to the mixed finite element method with flux error control in H(div). The paper gives an outline of the mathematical analysis for optimal convergence rates but also serves as a reference so that future contributions merely verify a few axioms in a new application in order to ensure optimal mesh-refinement of the adaptive algorithm.
收起
摘要 :
A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usu...
展开
A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a posteriori error estimation for this new method are also proved.
收起
摘要 :
Prediction and simulation of load-related reflective cracking in air field pavements require three-dimensional models in order to accurately capture the effects of gear loads on crack initiation and propagation. In this paper, we ...
展开
Prediction and simulation of load-related reflective cracking in air field pavements require three-dimensional models in order to accurately capture the effects of gear loads on crack initiation and propagation. In this paper, we demonstrate that the Generalized Finite Element Method (GFEM) enables the analysis of reflective cracking in a three-dimensional setting while requiring significantly less user intervention in model preparation than the standard FEM. As such, it provides support for the development of mechanistic-based design procedures for airfield overlays that are resistant to reflective cracking. Two gear loading positions of a Boeing 777 aircraft are considered in this study. The numerical simulations show that reflective cracks in airfield pavements are subjected to mixed mode behavior with all three modes present. They also demonstrate that under some loading conditions, the cracks exhibit significant channeling.
收起
摘要 :
We establish a general framework for analyzing the class of finite volume methods which employ continuous or totally discontinuous trial functions and piecewise constant test functions. Under the framework, optimal order convergen...
展开
We establish a general framework for analyzing the class of finite volume methods which employ continuous or totally discontinuous trial functions and piecewise constant test functions. Under the framework, optimal order convergence in the H1 and L2 norms can be obtained in a natural and systematic way for classical finite volume methods and new finite volume methods such as discontinuous finite volume methods applied to second order elliptic problems.
收起
摘要 :
This paper enfolds a medius analysis for the Stokes equations and compares different finite element methods (FEMs). A first result is a best approximation result for a P_1 non-conforming FEM. The main comparison result is that the...
展开
This paper enfolds a medius analysis for the Stokes equations and compares different finite element methods (FEMs). A first result is a best approximation result for a P_1 non-conforming FEM. The main comparison result is that the error of the P_2 P_0-FEM is a lower bound to the error of the Bernardi-Raugel (or reduced P_2P_0) FEM, which is a lower bound to the error of the P_1 non-conforming FEM, and this is a lower bound to the error of the MINI-FEM. The paper discusses the converse direction, as well as other methods such as the discontinuous Galerkin and pseudostress FEMs. Furthermore this paper provides counterexamples for equivalent convergence when different pressure approximations are considered. The mathematical arguments are various conforming companions as well as the discrete inf-sup condition.
收起
摘要 :
This work presents how approximate solution methods were introduced in a graduate level course of Theory of Elasticity. The three methods introduced are the finite difference method, the finite element method, and the boundary ele...
展开
This work presents how approximate solution methods were introduced in a graduate level course of Theory of Elasticity. The three methods introduced are the finite difference method, the finite element method, and the boundary element method. All methods are exemplified by the problem of a thick-walled cylinder subject to internal pressure with an axisymmetric response. Choosing a single problem to introduce the three methods demonstrates accuracy and efficacy of each method.
收起
摘要 :
This paper presents a comparative study on the available numerical approaches for modelling the fracturing of brittle materials. These modelling techniques encompass the finite element method (FEM), extended finite element method ...
展开
This paper presents a comparative study on the available numerical approaches for modelling the fracturing of brittle materials. These modelling techniques encompass the finite element method (FEM), extended finite element method (XFEM), discrete element method (DEM) and combined finite-discrete element method (FEM/DEM). This study investigates their inherent weaknesses and strengths for modelling the fracture and fragmentation process. A comparative review is first carried out to illustrate their fundamental principles as well as the advantages for the modelling of cracks, followed by the state-of-the-art trial application in the example cases. An example of a glass beam subjected to low velocity hard body impact is examined as a plane stress problem. By evaluating the applicability of different models, the most desirable model for the entire dynamic fracture response is identified, and this is found to be the FEM/DEM. The FEM/DEM model is further examined by comparing results with the experimental data from high velocity and oblique impact tests. The study reveals that the FEM/DEM yields the most satisfactory results when modelling the dynamic fracture process of brittle materials such as glass. (C) 2017 Elsevier Ltd. All rights reserved.
收起
摘要 :
Finite element analysis (FEA) is a commonly applied experimental research technique which enables us to study the effects of geometrical and material variations under load and internal mechanical process. In the last decade the ap...
展开
Finite element analysis (FEA) is a commonly applied experimental research technique which enables us to study the effects of geometrical and material variations under load and internal mechanical process. In the last decade the application of a well-proven predictive technique, the finite element method (FEM), originally used in structural analysis has revolutionized dental biomedical research.
收起
原文获取